Thursday, November 8, 2012

Ergodicity -- the Biggest Mistake in Economics?

I'm increasingly convinced that Ole Peters has identified the nub of an utterly essential problem in the framework of contemporary (i.e. last 50 years) economics. In a series of recent papers (here, here, here), he has argued with impressive clarity that the usual ensemble averages used to compute "expected" returns in finance are, in many cases, simply inappropriate to making decisions in the real world. Take a risky gamble, and the usual average over different outcomes mixes potential worlds in which we go broke with others in we get rich, and, importantly, takes the often irreversible consequences of these outcomes (bankruptcy, for example) out of the picture. If you make hugely risky investments, this average gives you full credit for all the wonderful possible outcomes, weighted appropriately for their likelihood, which of course seems sensible. What it doesn't do is account for the very real fact that the bad outcomes may effectively wipe you out entirely and take you out of the game, making it impossible to play again -- in which case you will never get to experience those eventual big payoffs.

Maybe the best thing to read about this is this wonderful paper by people from the financial firm Towers Watson (credit: I learned of this from Rick Bookstaber's blog). The potential implications of this are really huge, as Peters' perspective suggests that the standard way of assessing risk versus reward in financial economics is wrong and systematically underestimates risks (and not merely because it ignores fat tails). The paper above, the first paper of Peters I mentioned above, and this interview with Peters are among the most interesting things I've read this year.

I'm going to do an in depth post on this stuff soon, but I must admit that I need to study it in detail a little more. I'm convinced that Peters insight -- which brilliantly resolves the centuries old "St Petersburg paradox" of probability theory proposed originally by Bernoulli -- also has a lot to do with the work of Doyne Farmer and John Geanakoplos on economic discounting, which I've written about before. Both suggest that our basic thinking about probability in time series suffers from some terrible misconceptions, and generally makes us underestimate risks. More coming on this soon.